I read somewhere that oversampling somehow reduces sampling noise? How to quantify the reduction in noise? and why would it reduce noise if you are decimating the oversampled signal. What's the advantage of oversampling followed by decimation, verses just sampling the signal at the decimation rate to begin with? Or is the advantage moot, and its generally better to just sample at the decimation rate to begin with and forgo the oversampling. would there be a case where one is better than the other, and vica versa?
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4 Answers
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I may have originally misinterpreted your question so I'll change my answer here.
As to why we don't typically just sample at our a decimation rate (i.e. the Nyquist rate for the bandwidth of interest). It really comes down to the practicality:
If you had a 200hz signal of interest, yes you could sample at 400hz assuming there was absolute no noise in your system. However, there will be noise and you would need an anti-alias filter to block all frequencies greater than 200hz. The issue with this is that many anti-aliasing filters are slow roll-off because they're cheaper and easier to implement. Higher order analog filters are simply more expensive and difficult to implement (they're more sensitive to component tolerances).
Instead, it would make more sense for us to over-sample our signal such that we could use a lower order anti-alias filter.
Let's say your signal of interest is still 200hz and you decide to sample at 10khz this time. You put in an anti-alias filter at say 5kHz with a slow roll off. This would prevent aliasing frequencies of getting into your digital signal while being able to use a cheap/easy anti-alias filter. You would then perform your decimation operation. Note that the decimation operation includes a digital low-pass filter such that aliasing doesn't occur in the down-sampling process.
Summary: the further we separate our bandwidth of interest from the Nyquist rate, we can use lower-order anti-alias filters which are cheaper to implement.
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$\begingroup$ ok nyquist theorm... i get it... but you could also sample 200 hz sinewave at 400 hz... but maybe that's too aggressive...so let's say we sample 200 hz sine at 800hz... is it better to oversample at 20Khz then decimate to 800 hz? or just sample at 800 hz directly? (assuming an ideal world where an ADC can sample at any clock rate) $\endgroup$ Commented Apr 15, 2019 at 19:33
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$\begingroup$ @BillMoore I changed my response because i misinterpreted the question. Hopefully it makes more sense now. Essentially a higher sample rate allows us to simplify the analog portion of our electronics design. $\endgroup$– IzzoCommented Apr 15, 2019 at 19:53
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You can gain a bit of resolution by 4X increase of sampling rate without doing anything special.
The basic idea depends on quantization noise being flat and filtering out the nonsignal part of the acquired spectrum digitally.
Modern A/D converters use a feedback technique called noise shaping to increase resolution.
One should understand that converter resolution is a separate issue from Nyquist band limiting but oversamplng does make antialiasing filtering less demanding.
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Simply put it moves more of the processing to digital domain which is more accurate and more controlled. This way the analog components (filters) before ADC and after DAC can be simpler and the circuit will perform better and can use less parts, cheaper parts and parts with less tolerance.
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Sampling at a higher rate (say multiples above the Nyquist rate for the desired final bandwidth) provides more bits of information per unit time about the signal of interest.
Now if the signal is roughly band-limited for that lower sample rate, most, perhaps all of those extra bits are redundant and do not increase the information content of the samples much, or at all. The greater number of samples in a time interval might be identical.
But if there is a small amount of additive noise (say in the neighborhood of 1 LSB), or a local slope, a few, maybe only 1 bit, of those extra LSB’s from the greater number of samples might be changing, and thus won’t be completely redundant. A suitable digital anti-alias filter for the new lower final decimated rate might be able to extract some of that information and perhaps put it into a larger destination format (say into float or double, noise-filter-decimated from a larger set of 8 or 16 bit samples taken at the original higher sample rate, etc.). That could be considered a reduction in quantization noise compared to a simple int to float conversion of samples taken at just above the Nyquist rate.
